Notes - Linear Algebra I MT22, Chapter 6

Created: December 31, 2022

  • [[Course - Linear Algebra I MT22]]U
  • Content covered:
    • Prove a linear map is invertible if and only if it is bijective (Prop. 154)
    • Prove there exists an invertible linear map between two finite dimensional vector spaces if they have the same dimension. (Prop. 156)
    • Prove lots of properties about the kernel and image relating to subspaces (Prop. 159)
    • Prove the rank nullity theorem (The. 162).

Flashcards

What’s the useful inequality about the nullity composition of two linear maps?
\[\text{null}(ST) \le \text{null}(S) + \text{null}(T)\]

What’s the useful inequality about the rank of the sum of two linear maps?
\[\text{rank}(S + T) \le \text{rank}(S) + \text{rank}(T)\]


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